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arXiv physics/0304111physics.flu-dynphysics.class-ph
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预混火焰的大尺度演化

Large Scale Evolution of Premixed Flames

Kirill A. Kazakov

摘要:

研究了预混火焰的小尺度“蜂窝状”结构对其在大尺度上演化的影响。本文介绍了一种对火焰单元上的流动变量进行时空平均的方法。证明了在火焰前缘厚度的第一阶中,平均气体速度和压力的动力学方程的形式以及火焰前缘处这些量的跳跃条件与零厚度火焰在相对于燃料以恒定速度传播的理想流体中的情况相同,等于平面火焰的绝热速度乘以一个描述由于局部前缘扭曲而导致的火焰前缘长度增加的因子。作为应用,研究了火焰在引力场中的大尺度演化。推导出平均火焰前锋位置的弱非线性非定常方程。研究发现,主导的非线性引力效应稳定了火焰沿场方向的传播。由此产生的固定火焰配置确定解析。

英文摘要:

The influence of the small scale ``cellular'' structure of premixed flames on their evolution at larger scales is investigated. A procedure of the space-time averaging of the flow variables over flame cells is introduced. It is proved that to the leading order in the flame front thickness, the form of dynamical equations for the averaged gas velocity and pressure, as well as of jump conditions for these quantities at the flame front, is the same as in the case of a zero-thickness flame propagating in an ideal fluid at constant velocity with respect to the fuel, equal to the adiabatic velocity of a plane flame times a factor describing increase of the flame front length due to the local front wrinkling. As an application, the large scale evolution of a flame in the gravitational field is investigated. A weakly nonlinear non-stationary equation for the averaged flame front position is derived. It is found that the leading nonlinear gravitational effects stabilize the flame propagating in the direction of the field. The resulting stationary flame configurations are determined analytically.

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